Controller reduction by H∞ balanced truncation for infinite-dimensional, discrete-time systems

We consider Lyapunov and H ∞ balancing as well as model reduction by balanced truncation for infinite-dimensional, discrete-time linear systems. A functional analytic approach to state space transformation leading to balanced realization is presented. Furthermore, we show that a finite-dimensional H ∞ controller designed for a H ∞ balanced and truncated system stabilizes the original infinite-dimensional system, provided the error made by this model reduction procedure is small enough.